Influence of the Use of Exact Line Search on the Convergence of Accelerated Proximal Gradient Methods

• Grant number: 25/12023-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2025
• End date: August 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Elias Salomão Helou Neto
• Grantee: Gabriel Ligabô Baba
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Optimization methods are a key component in medical image reconstruction, especially in computed tomography. The data acquired by this technique consists of a noisy sampling of the Radon transform, which necessitates the inclusion of regularization terms in the optimization model to prevent the noise in the data from being excessively amplified in the reconstructed image. Many potential choices for the regularization term are non-smooth, yet convex and prox-friendly, leading to the use of accelerated proximal gradient optimization algorithms. This project addresses a specific and underexplored aspect: we propose replacing the usual step size strategies (e.g., fixed step size or inexact line search with sufficient decrease criterion) in the FISTA (Fast Iterative Shrinkage-Thresholding Algorithm). Instead, we will investigate the use of an exact line search to determine the step size. Specifically, we will use a least squares term for the data consistency component and analytically compute the step size that minimizes this component along the direction of steepest descent. The goal is to objectively measure how this choice affects convergence in terms of iterations and computation time, as well as the reconstruction quality in computed tomography data. (AU)